Mechanical Engineering - Strength of Materials - Discussion
Discussion Forum : Strength of Materials - Section 2 (Q.No. 19)
19.
The bending moment of a cantilever beam of length l and carrying a gradually varying load from zero at free end and w per unit length at the fixed end is __________ at the fixed end.
Discussion:
6 comments Page 1 of 1.
Jay said:
9 years ago
Shear force at section XX.
F x = + 1/2 *(w/l) * x *x (area of loading between B and xx).
=+ wx2/2l.
SF at B, FB = 0, Whereas x = 0,
SF at A, FA =+ wl/ 2 , whereas x = l.
The shear force diagram is in form of parabolic curve like the shear force equation is a parabolic equation.
Bending moment at section XX.
Mx =- (1/2) * (w/l) x (1/3) x (Moment of the area loading between B and XX).
=- wx3/6l (that means area * CG of loading diagram around XX).
BM at B, MB = 0 (Whereas x = 0), and BM at A,
Mx =- wl2/6 (when x = l).
F x = + 1/2 *(w/l) * x *x (area of loading between B and xx).
=+ wx2/2l.
SF at B, FB = 0, Whereas x = 0,
SF at A, FA =+ wl/ 2 , whereas x = l.
The shear force diagram is in form of parabolic curve like the shear force equation is a parabolic equation.
Bending moment at section XX.
Mx =- (1/2) * (w/l) x (1/3) x (Moment of the area loading between B and XX).
=- wx3/6l (that means area * CG of loading diagram around XX).
BM at B, MB = 0 (Whereas x = 0), and BM at A,
Mx =- wl2/6 (when x = l).
Nagesh said:
8 years ago
First convert varying load to point load = 1/2*w*l = wl/2.
B.m=(wl/2)*(1/3rd of total length from highest load point) =(wl/2)*(l/3)= wl^2/6.
B.m=(wl/2)*(1/3rd of total length from highest load point) =(wl/2)*(l/3)= wl^2/6.
Venkatesh K said:
1 decade ago
Varying force = W*L/2.
Bending Moment(M) = (W*L/2)(L/3) = W*L^2/6.
Bending Moment(M) = (W*L/2)(L/3) = W*L^2/6.
Ananth said:
9 years ago
How L/3 came? explain me @Venkatesh.
Devansh said:
5 years ago
Nice, Thanks @Venkatesh.
Jithu said:
9 years ago
Nice @Venkatesh.
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